A DC Programming Approach for Worst-Case Secrecy Rate Maximization Problem | SpringerLink
Skip to main content

A DC Programming Approach for Worst-Case Secrecy Rate Maximization Problem

  • Conference paper
  • First Online:
Computational Collective Intelligence (ICCCI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11055))

Included in the following conference series:

  • 1333 Accesses

Abstract

This paper is concerned with the problem of secure transmission for amplify-and-forward multi-antenna relay systems in the presence of multiple eavesdroppers. Specifically, spatial beamforming and artificial noise broadcasting are chosen as the strategy for secure transmission with robustness against imperfect channel state information of the intended receiver and the eavesdroppers. In such a scenario, the objective is to maximize the worst-case secrecy rate while guaranteeing the transmit power constraint at the relay and the norm-bounded channel uncertainty. We reformulate the problem as a general DC (Difference-of-Convex functions) program (i.e. minimizing a DC function under DC constraints) and develop a very inexpensive DCA based algorithm for solving it. Numerical results illustrate the effectiveness of the proposed algorithm and its superiority versus the existing approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Kumar, S., Paar, C., Pelzl, J., Pfeiffer, G., Ruppp, A., Schimmler, M.: How to break DES for euro 8,980. In: Workshop on Special purpose Hardware for Attacking Cryptographic Systems – SHARCS 2006, Colgne, Germany (2006)

    Google Scholar 

  2. Li, Q., Song, H., Huang, K.: Achieving secure transmission with equivalent multiplicative noise in MISO wiretap channels. IEEE Commun. Lett. 17(5), 892–895 (2013)

    Article  Google Scholar 

  3. Wyner, A.D.: The wire-tap channel. Bell Syst. Tech. J. 54(8), 1355–1387 (1975)

    Article  MathSciNet  Google Scholar 

  4. Leung-Yan-Cheong, S., Hellman, M.E.: The Gaussian wiretap channel. IEEE Trans. Inf. Theory 24(7), 451–456 (1978)

    Article  Google Scholar 

  5. Zou, Y., Wang, X., Shen, W.: Eavesdropping attack in collaborative wireless networks: security protocols and intercept behavior. In: Proceedings of the 17th IEEE International Conference on Computer Supported Cooperative Work in Design, Whistler, Canada, pp. 704–709 (2013)

    Google Scholar 

  6. Zhang, J., Gursoy, M.: Collaborative relay beamforming for secrecy. In: Proceedings of the IEEE Wireless Communication Symposium (ICC), Cape Town, South Africa, pp. 1–5 (2010)

    Google Scholar 

  7. Jeong, C., Kim, I., Dong, K.: Joint secure beamforming design at the source and the relay for an amplify-and-forward MIMO untrusted relay system. IEEE Trans. Signal Process. 60(1), 310–325 (2012)

    Article  MathSciNet  Google Scholar 

  8. Mukherjee, A., Swindlehurst, A.: Robust beamforming for security in MIMO wiretap channels with imperfect CSI. IEEE Trans. Signal Process. 59(1), 351–361 (2011)

    Article  MathSciNet  Google Scholar 

  9. Goel, S., Negi, R.: Guaranteeing secrecy using artificial noise. IEEE. Trans. Wireless Commun. 7(6), 2180–2189 (2008)

    Article  Google Scholar 

  10. Li, Q., Yang, Y., Ma, W.K., Lin, M., Ge, J., Lin, J.: Robust cooperative beamforming and artificial noise design for physical-layer secrecy in AF multi-antenna multi-relay networks. IEEE Trans. Signal Process. 63(1), 206–220 (2015)

    Article  MathSciNet  Google Scholar 

  11. Zhang, C., Gao, H., Liu, H., Lv, T.: Robust beamforming and jamming for secure AF relay networks with multiple eavesdroppers. In: IEEE Military Communications Conference (MILCOM), pp. 495–500 (2014)

    Google Scholar 

  12. Zhang, L., Jin, L., Luo, W., Tang, Y., Yu, D.: Robust joint beamforming and artificial noise design for amplify-and-forward multi-antenna relay systems. In: IEEE Speech and Signal Processing (ICASSP), pp. 1732–1736 (2015)

    Google Scholar 

  13. Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: theory, algorithms and applications. Acta Mathematica Vietnamica 22, 289–355 (1997)

    MathSciNet  MATH  Google Scholar 

  14. Pham Dinh, T., Le Thi, H.A.: DC optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8, 476–505 (1998)

    Article  MathSciNet  Google Scholar 

  15. Pham Dinh, T., Le Thi, H.A.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world non convex optimization problems. Ann. Oper. Res. 133, 23–46 (2005)

    Article  MathSciNet  Google Scholar 

  16. Le Thi, H.A., Huynh, V.N., Pham Dinh, T.: DC Programming and DCA for General DC Programs. In: van Do T., Thi H., Nguyen N. (eds) Advanced Computational Methods for Knowledge Engineering. Advances in Intelligent Systems and Computing, pp. 15–35 (2014)

    Google Scholar 

  17. Pham Dinh, T., Le Thi, H.A.: Recent advances in DC programming and DCA. Trans. Comput. Intell. 13, 1–37 (2014)

    Google Scholar 

  18. Le Thi, H.A., Pham Dinh, T.: DC programming and DCA: thirty years of developments. Math. Program. 169(1), 5–68 (2018). Special Issue: DC Programming - Theory, Algorithms and Applications

    Article  MathSciNet  Google Scholar 

  19. Grant, M., Boyd, S: CVX: Matlab software for disciplined convex programming, version 2.0 (2012). http://cvxr.com/cvx

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Phuong Anh Nguyen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Nguyen, P.A., Le Thi, H.A. (2018). A DC Programming Approach for Worst-Case Secrecy Rate Maximization Problem. In: Nguyen, N., Pimenidis, E., Khan, Z., Trawiński, B. (eds) Computational Collective Intelligence. ICCCI 2018. Lecture Notes in Computer Science(), vol 11055. Springer, Cham. https://doi.org/10.1007/978-3-319-98443-8_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-98443-8_38

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-98442-1

  • Online ISBN: 978-3-319-98443-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics